On the Mellin transforms of powers of Hardy's function.
Authors: Aleksandar Ivić 1
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Aleksandar Ivić
1 Katedra Matematike
Various properties of the Mellin transform function
$$\mathcal{M}_k(s):= \int_1^{\infty} Z^k(x)x^{-s}\,dx$$
are investigated, where $$Z(t):=\zeta(\frac{1}{2}+it)\,\chi(\frac{1}{2}+it)^{-1/2},~~~~\zeta(s)=\chi(s)\zeta(1-s)$$
is Hardy's function. Connections with power moments of $|\zeta(\frac{1}{2}+it)|$ are established, and natural boundaries of $\mathcal{M}_k(s)$ are discussed.
The Mellin transform of the square of Riemann's zeta-function
2 Documents citing this article
Source : OpenCitations
IviÄ, Aleksandar, 2010, On Some Problems Involving Hardyâs Function, Central European Journal Of Mathematics, 8, 6, pp. 1029-1040, 10.2478/s11533-010-0071-y.
Jutila, M., 2010, The Mellin Transform Of Hardyâs Function Is Entire, Mathematical Notes, 88, 3-4, pp. 612-616, 10.1134/s0001434610090348.